www.gusucode.com > nncontrol 工具箱 matlab 源码程序 > nncontrol/csrchbre.m
function [up_delta,J,dJdu_old,dJdu,retcode,delta,tol] = csrchbre(up,u_vec,ref,Ai,Nu,N1,N2,d,Ni,Nj,dX, ...
dJdu,J,dperf,delta,rho,dUtilde_dU,alpha,tol,Ts,min_i,max_i,Normalize,minp,maxp)
%CSRCHBRE One-dimensional interval location using Brent's method.
%
% Syntax
%
% [up_delta,J,dJdu_old,dJdu,retcode,delta,tol] = csrchbre(up,u_vec,ref,Ai,Nu,N1,N2,d,Ni,Nj,dX, ...
% dJdu,J,dperf,delta,rho,dUtilde_dU,alpha,tol,Ts,min_i,max_i,Normalize)
%
% Description
%
% CSRCHBRE is a linear search routine. It searches in a given direction
% to locate the minimum of the performance function in that direction.
% It uses a technique called Brent's method.
%
% CSRCHBRE(...) takes these inputs,
% up - Plant Inputs during the Control Horizon (Nu).
% u - Plant Inputs during the Cost Horizon (N2).
% ref - Reference input.
% Ai - Initial input delay conditions.
% Nu - Control Horizon.
% N1 - Beginning of the Control and Cost Horizons (Usually 1).
% N2 - Cost Horizon.
% d - Counter that defined initial time (Usually 1).
% Ni - Number of delayed plant inputs.
% Nj - Number of delayed plant outputs.
% dX - Search direction vector for U.
% dJdu - Derivate of the cost function respect U.
% J - Cost function value.
% dperfa - Slope of performance value at current U in direction of dX.
% delta - Initial step size.
% rho - Control weighting factor.
% dUtlde_dU - Derivate of the difference of U(t)-U(t-1) respect U.
% alpha - Search parameter.
% tol - Tolerance on search.
% Ts - Time steps.
% min_i - Minimum Input to the Plant.
% max_i - Maximum Input to the Plant.
% Normalize - Indicate if the NN has input-output normalized.
% and returns,
% up_delta - New Plant Inputs for the Control Horizon (Nu).
% J - New Cost function value.
% dJdu_old - Previous Derivate of the cost function respect U.
% dJdu - New Derivate of the cost function respect U.
% RETCODE - Return code which has three elements. The first two elements correspond to
% the number of function evaluations in the two stages of the search
% The third element is a return code. These will have different meanings
% for different search algorithms. Some may not be used in this function.
% 0 - normal; 1 - minimum step taken; 2 - maximum step taken;
% 3 - beta condition not met.
% DELTA - New initial step size. Based on the current step size.
% TOL - New tolerance on search.
%
% Parameters used for the brent algorithm are:
% alpha - Scale factor which determines sufficient reduction in perf.
% beta - Scale factor which determines sufficiently large step size.
% bmax - Largest step size.
% scale_tol - Parameter which relates the tolerance tol to the initial step
% size delta. Usually set to 20.
% The defaults for these parameters are set in the training function which
% calls it. See TRAINCGF, TRAINCGB, TRAINCGP, TRAINBFG, TRAINOSS
%
% Algorithm
%
% CSRCHBRE brackets the minimum of the performance function in
% the search direction dX, using Brent's
% algorithm described on page 46 of Scales (Introduction to
% Non-Linear Estimation 1985). It is a hybrid algorithm based on
% the golden section search and quadratic approximation.
%
% See also CSRCHBAC, CSRCHCHA, CSRCHGOL, CSRCHHYB
%
% References
%
% Brent, Introduction to Non-Linear Estimation, 1985.
% Orlando De Jesus, Martin Hagan, 1-30-00
% Copyright 1992-2002 The MathWorks, Inc.
tiu = d-N1+Ni;
upi = [1:Nu-1 Nu(ones(1,N2-d-Nu+2))]; % [1 2 ... Nu Nu ... Nu]
uvi = [tiu:N2-N1+Ni];
% ALGORITHM PARAMETERS
scale_tol = 20;
beta = 0.1;
bmax = 26;
delta_orig=delta;
%INITIALIZE
perfa = J;
a = 0;
u = 1e19;
perfu = 1e19;
cnt1 = 0;
cnt2 = 0;
lambda = delta;
% INTERVAL FOR GOLDEN SECTION SEARCH
tau = 0.618;
tau1 = 1 - tau;
% STEP SIZE INCREASE FACTOR FOR INTERVAL LOCATION (NORMALLY 2)
scale = 2;
% INITIALIZE A AND B
a = 0;
a_old = 0;
b = delta;
perfa = J;
perfa_old = perfa;
up_delta = max(min(up + b*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR B
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfb = JJ;
dJdub = dJJ;
cnt1 = cnt1 + 1;
% INTERVAL LOCATION
% FIND INITIAL INTERVAL WHERE MINIMUM PERF OCCURS
while (perfa>perfb)&(b<bmax)
a_old=a;
perfa_old=perfa;
perfa=perfb;
a=b;
b=scale*b;
up_delta = max(min(up + b*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR B
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfb = JJ;
dJdub = dJJ;
cnt1 = cnt1 + 1;
end
if (a == a_old)
% GET INTERMEDIATE POINT IF NO MIDPOINT EXISTS
v = a + tau1*(b - a);
w = v;
x = v;
up_delta = max(min(up + v*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR V
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfv = JJ;
dJduv = dJJ;
perfw = perfv;
perfx = perfv;
cnt1 = cnt1 + 1;
else
% USE ALREADY COMPUTED VALUE AS INITIAL INTERMEDIATE POINT
v = a;
w = v;
x = v;
perfv = perfa;
perfw = perfv;
perfx = perfv;
a=a_old;
perfa=perfa_old;
end
max_int = w;
min_int = w;
% REDUCE THE INTERVAL
while ((b-a)>tol) & (perfx >= J + alpha*x*dperf)
% QUADRATIC INTERPOLATION
if (w~=x)&(w~=v)&(x~=v)&( (max_int - min_int) > 0.02*(b-a) )
[zz,i] = sort([v w x]);
pp = [perfv perfw perfx];
pp = pp(i);
num = (zz(3)^2 - zz(2)^2)*pp(1) + (zz(2)^2 - zz(1)^2)*pp(3) + (zz(1)^2 - zz(3)^2)*pp(2);
den = (zz(3) - zz(2))*pp(1) + (zz(2) - zz(1))*pp(3) + (zz(1) - zz(3))*pp(2);
if den==0
x_star=Inf; % ODJ: 1-30-00 If den = 0 then x_star = Inf.
else
x_star = 0.5*num/den;
end
if (x_star < b)&(a < x_star)
u = x_star;
gold_sec = 0;
else
gold_sec = 1;
end
else
gold_sec = 1;
end
% GOLDEN SECTION
if (gold_sec == 1)
if (x >= (a + b)/2);
u = x - tau1*(x - a);
else
u = x + tau1*(b - x);
end
end
up_delta = max(min(up + u*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR B
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfu = JJ;
dJduu = dJJ;
cnt2 = cnt2 + 1;
% UPDATE POINTS
if (perfu <= perfx)
if (u < x)
b = x;
perfb = perfx;
else
a = x;
perfa = perfx;
end
v = w; perfv = perfw;
w = x; perfw = perfx;
x = u; perfx = perfu;
else
if (u < x)
a = u;
perfa = perfu;
else
b = u;
perfb = perfu;
end
if (perfu <= perfw) | (w == x)
v = w; perfv = perfw;
w = u; perfw = perfu;
elseif (perfu <= perfv) | (v == x) | (v == w)
v = u; perfv = perfu;
end
end
temp = [w x v];
min_int = min(temp);
max_int = max(temp);
end
% COMPUTE THE FINAL STEP, FUNCTION VALUE AND GRADIENT
xtot = [a b v w x];
perftot = [perfa perfb perfv perfw perfx];
[perftot,i] = sort(perftot);
xtot = xtot(i);
a = xtot(1);
up_delta = max(min(up + a*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR A
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
J = JJ;
dJdu_old=dJdu;
dJdu = dJJ;
% CHANGE INITIAL STEP SIZE TO PREVIOUS STEP
delta=a;
if delta < delta_orig
delta = delta_orig;
end
if tol>delta/scale_tol
tol=delta/scale_tol;
end
retcode = [cnt1 cnt2 0];